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The Emergence of Rational Behavior in the Presence of Stochastic Perturbations

Abstract : We study repeated games where players use an exponential learning scheme in order to adapt to an ever-changing environment. If the game's payoffs are subject to random perturbations, this scheme leads to a new stochastic version of the replicator dynamics that is quite different from the ``aggregate shocks'' approach of evolutionary game theory. Irrespective of the perturba- tions' magnitude, we find that strategies which are dominated (even iteratively) eventually become extinct and that the game's strict Nash equilibria are stochastically asymptotically stable. We complement our analysis by illustrating these results in the case of congestion games.
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https://hal.archives-ouvertes.fr/hal-01382306
Contributor : Panayotis Mertikopoulos <>
Submitted on : Sunday, October 16, 2016 - 3:29:26 PM
Last modification on : Monday, March 16, 2020 - 4:40:04 PM

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  • HAL Id : hal-01382306, version 1

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Panayotis Mertikopoulos, Aris L. Moustakas. The Emergence of Rational Behavior in the Presence of Stochastic Perturbations. Annals of Applied Probability, Institute of Mathematical Statistics (IMS), 2010, 20 (4), pp.1359-1388. ⟨hal-01382306⟩

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